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\author{Linjie Zheng}
\affiliation[Universit\'e de Toulouse (UPS) and CNRS]{Laboratoire de Chimie et Physique Quantiques LCPQ/IRSAMC, Universit\'e de Toulouse (UPS) and CNRS, 118 Route de Narbonne, F-31062 Toulouse, France}
\author{Mathias Rapacioli}
\affiliation[Universit\'e de Toulouse (UPS) and CNRS]{Laboratoire de Chimie et Physique Quantiques LCPQ/IRSAMC, Universit\'e de Toulouse (UPS) and CNRS, 118 Route de Narbonne, F-31062 Toulouse, France}
\author{Fernand Louisnard}
\affiliation[Universit\'e de Toulouse (UPS) and CNRS]{Laboratoire de Chimie et Physique Quantiques LCPQ/IRSAMC, Universit\'e de Toulouse (UPS) and CNRS, 118 Route de Narbonne, F-31062 Toulouse, France}
\author{J\'er\^ome Cuny}
\affiliation[Universit\'e de Toulouse (UPS) and CNRS]{Laboratoire de Chimie et Physique Quantiques LCPQ/IRSAMC, Universit\'e de Toulouse (UPS) and CNRS, 118 Route de Narbonne, F-31062 Toulouse, France}
\email{jerome.cuny@irsamc.ups-tlse.fr}
\phone{+33 (0)5 61 55 68 36}
\fax{+33 (0)5 61 55 60 65}

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\title[An \textsf{achemso} demo]
{A dynamics collision simulation study on proton localization of uracil protonated water clusters\footnote{A dynamics collision simulation study on proton localization of uracil protonated water clusters}}

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%\abbreviations{PES,ISM,COSAC,FT-IR,MRCI+Q,CCD,CCSD(T),RCCSD(T),UCCSD(T),MP2, MBPT, BSSE, ZPE, DFT, SCC-DFTB, CM3, MD, MDPT}
\keywords{Molecular Dynamics, SCC-DFTB, Collision Induced Dissociation, Uracil Protonated Water Clusters}

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\begin{abstract}
A series of dynamics collision simulations between lowest-energy uracil protonated water clusters (H$_2$O)$_{n=3-7, 12}$UH$^+$ and Argon atom were performed with the self-consistent-charge density-functional based tight-binding (SCC-DFTB) method to make a deep exploration of the collision process. From the dynamics collision simulations, the trend of different types of fragments and location of the excess proton were observed. Our initial geometries provided a reasonably uniform distribution of Argon projectiles around each uracil protonated water clusters leading Argon atom can collide at all the possible positions of each cluster. The theoretical simulation data show that the proportion of neutral uracil molecule loss and total fragmentation cross sections are consistent with those in experiment. Additionally, we observed that up to 7 water molecules the clusters had a direct dissociation mechanism after collision \blue{whereas for 12 water molecules …...} Furthermore, the calculation results indicate the excess proton location is highly dependent on the initial isomer as stated in a previous study. \blue{By conducting path-integral MD simulation, we finally observed that nuclear quantum effect XXX.} \blue{We are the first to perform this kind of simulation,} our dynamics collision simulations for predicting the type and amount of fragments and fragmentation cross sections of collision system provide a useful tool. 
\end{abstract}

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\section{Introduction }

The nucleobases in DNA and RNA play a very important role in the encoding and expression of genetic information in living systems while water represents the natural medium of many reactions in living organisms. Therefore, it is a significant point to study the interaction between nucleobase molecules and aqueous environment. 
The radiation effect on RNA and DNA molecules is still a medical challenge in modern times. The radiation can cause damages on these molecules. Radiation damages are proficiently applied in radiotherapy for cancer treatment. The major drawback in radiotherapy is the unselective damage in both healthy and tumor cells, which has a big side effect. This makes it particularly important to explore the radiation fragments. RNA nucleobase, uracil C$_4$H$_4$N$_2$O$_2$ (U), has attracted scientist’s attention a lot. Protonated uracil UH$^+$ can be generated by radiation damages. Through the study of hydration effects on cytosine, uracil, and thymine pyrimidines by including one and two water molecules explicitly, Schaefer III \textit{et al.} found that a water molecule is more likely to interact with a charged species than with a neutral one.\cite{Rasmussen2010} However, the study about protonated necleobases in aqueous environment is not so much.  
  JC  MUCH BLABLA 
JC Add a sentence to say hydration of molecules can help to do something in real life

Studying hydration of molecules and biomolecules is of paramount important to get insights into their behavior in aqueous medium, in particular their structure, stability and dynamics. To do so, gas phase investigations of molecules play an important role in understanding the intrinsic properties of molecules, which is free from the effects of solvents or other factors. It allows to study the evolution of this behavior as the function of the hydration degree of the molecule and also probe the influence of the  protonated state.
Collision experiments in the gas phase is a useful tool that can be applied to provide structural information about molecular species.\cite{Coates2018} For instance, considering U molecule, which has attracted scientist’s attention a lot due to its important role in the encoding and expression of genetic information in living systems, various collision experiments have been conducted. Fragmentation of halogen substituted uracil molecules in the gas phase through collisions experiments have been performed.\cite{Imhoff2007,Abdoul2000,Champeaux2010,Delaunay2014} The theoretical calculations about the charge-transfer processes induced by collision have been also reported.\cite{Bacchus2009, Kossoski2015} Nevertheless, the gas phase study needs to be extended towards more realistic biomolecular systems, to reveal how the intrinsic molecular properties are affected by the surrounding medium when the biomolecules are in a natural environment.\cite{Maclot2011, Domaracka2012, Markush2016, Castrovilli2017}
 (JC, make this part smaller) 

It is reported that many collision experiments have been made via threshold collision-induced dissociation (TCID) for the hermodynamic information, electron ionization and fragmentation, binding energies and other properties of biomolecules.\cite{Hayes1990, Coates2017, Neustetter2017, Coates2018} Fragmentation of isolated protonated uracil has been studied through collision-induced dissociation (CID) with tandem mass sepctrometry, \cite{Nelson1994, Molina2015, Molina2016, Sadr2014} however, there are few studies concerning the surrounding aqueous environment effect on such collision process in experiment. Some theory studies have been performed about this but those studies have been limited to small water clusters. \cite{Bakker2008} Recently, Zamith’s group in collaboration with our group reported the CID experiment on uracil protonated water clusters (H$_2$O)$_{n=1-15}$UH$^+$ and theoretical study to determine the lowest-energy structures. \cite{Braud2019} In Zamith’s experiment, the collisions only lead to intermolecular bond breaking rather than intramolecular bond breaking in the (H$_2$O)$_{n=1-15}$UH$^+$ clusters. The collisions were performed with with(H$_2$O)$_{n=1-15}$UH$^+$ clusters and M= H$_2$O, D$_2$O, Ne, and Ar. They found no matter which M was used, the results were the same. They only showed the results with Ne. The branching ratios of different charged fragments were determined through mass spectra of the collision products. Fragmentation cross section of (H$_2$O)$_{n=1-15}$UH$^+$ clusters were obtained at a collision energy 7.2 eV as a function of the total number molecules in the clusters. The proportion of neutral uracil molecules loss were detected as a function of the number n of water molecules in the (H$_2$O)$_{n=1-15}$UH$^+$ clusters at 7.2 eV of mass collision energy. From the proportion results of neutral uracil molecules loss, it shows where the excess proton lies after collision. An obvious growth of neutral uracil molecules loss was observed from n = 5-6. Those experiment were complemented by theoretical calculations that aim at finding the lowest-energy (H$_2$O)$_{n=1-7}$UH$^+$ clusters. From the structures of lowest-energy isomers, it clearly shows that (i) for small clusters (when n = 1-2), the excess proton is on the uracil; (ii) for n = 3-4, the excess proton is still on the uracil but it has a tendency to be displaced towards adjacent water molecules; (iii) when n is larger than 4, the excess proton is completely transferred to the water clusters. These results are in full agreement with the CID measurements.

However, although the location of the excess proton in lowest-energy isomers is clear, there are still some issues that need to be settled: (i) What’s the main path of the fragmentation mechanisms? (ii) What are the fragments after the collision? (iii) How does the proportion of the fragments change according to the time? (iv) If the proportion of neutral uracil molecules loss only determined by the lowest-energy isomers? With interests in these questions, it pursues us to do an explicit dynamics exploration for these uracil protonated water clusters. 

Some studies have already been done about the dynamics collision simulation.\cite{Tomsic2013,  Korchagina2017, Simon2017, Rapacioli2018} In the present work, we made the dynamics simulation to investigate the collision of (H$_2$O)$_{n=3-7, 12}$UH$^+$ clusters and Ar. Based on the dynamics collision simulations, we analyzed the fragmentation cross section of mixed (H$_2$O)$_{n=3-7, 12}$UH$^+$ clusters according to the total number molecules in the clusters. The branching ratios of different charged fragments were explored of the collision products. The proportion of neutral uracil molecules loss in the mixed (H$_2$O)$_{n=3-7, 12}$UH$^+$ clusters were also investigated. From all the above investigations, the two fragmentation mechanisms after collision, the mixed cluster has an immediately direct dissociation and the mixed cluster has a longer life before completed dissociation, which one is dominant is clear.
\blue{All simulations are performed in the microcanonical ensemble within the Born–Oppenheimer??}


\section{Computational Methods} \label{Comput_meth}
\textbf{Exploration of the PES}

DFTB is approximated from DFT scheme whose efficiency relies on the use of parameterized integrals with a much lower computational cost. \cite{Elstner2014} The DFTB approach has been particularly well studied and it has already proven its efficiency to describe chemical processes. \cite{Kruger2005} In this work, we used the second-order version of DFTB, Self Consistent Charge DFTB, with the mio-set for the Slater-Koster tables of integrals. \cite{Elstner1998} To improve the intermolecular interaction, the class IV/charge model 3 (CM3) charges instead of the original Mulliken charges as well as the empirical terms were used to describe dispersion interactions. \cite{Rapacioli2009} For the parameterization of CM3 charges, the bond parameter D$_{OH}$ = 0.129 proposed by Simon and co-workers was applied, \blue{DNH = 0.120 tested by ourselves, (part of this work has been published[])} while all other bond parameter values were set to be 0.000, which corresponds to a Mulliken evaluation of the charges.\cite{Simon2012, Simon2013} All the SCC-DFTB calculations in the present work were carried out with the deMonNano code. \cite{demonnanoCode}

All the energy minima for (H$_2$O)$_{n=3-7}$UH$^+$, have already been obtained in the previous study.\cite{Braud2019} In this present work, we calculated the lowest-energy isomers of (H$_2$O)$_{12}$UH$^+$ cluster. To obtain them, the same two-step theoretical method with the one used for the calculation of lowest energy isomers of clusters (H$_2$O)$_{n=1-7}$UH$^+$ was applied.\cite{Braud2019} Firstly, the potential energy surface (PES) of (H$_2$O)$_{12}$UH$^+$ was roughly explored using the parallel temperature molecular dynamics (PTMD) simulations in combination with SCC-DFTB description of the energies and gradients.\cite{Sugita1999, Earl2005} In the PTMD algorithm, 40 replicas with temperatures going linearly from 50 to 350 K were carried out. All the trajectories were 4 ns long, and the integration time step was 0.5 fs. A Nosé-Hoover chain of five thermostats with frequencies of 800 cm$^{-1}$ was used to obtain an exploration in the canonical emsemble. \cite{Nose1984, Hoover1985} To avoid any spurious influence of the initial geometry on the PES exploration, three distinct PTMD simulations were carried out. In the three series, a distinct initial proton location was set: on the uracil in two cases and on the water cluster in another one. In the former cases, the u178 and u138 UH$^+$ isomers were used as initial geometries which was named by Pedersen \cite{Pedersen2014}. 600 geometries per temperature were linearly selected along each PTMD simulation for subsequent geometry optimization leading to 72000 structures optimized at SCC-DFTB level. These structures were sorted in ascending energy order. Secondly, 29 isomers were selected from the 72000 optimized structures at SCC-DFTB level and were optimized at a high accurate MP2/Def2TZVP level, which is a tight criteria for geometry convergence and an ultrafine grid for the numerical integration. \cite{Weigend2005, Weigend2006} From the MP2/Def2TZVP calculation, the lowest energy isomers of cluster (H$_2$O)$_{12}$UH$^+$ were obtained. All MP2 calculations were carried out with the Gaussian 09 package.\cite{GaussianCode}

\textbf{Dynamics Collision Simulations} 

QM/MM method was used to describe the collision process of uracil protonated water cluster (QM) and Argon atom (MM) in the developed deMonNano code.\cite{Warshel1976} In the dynamics collision calculation, a Fermi distribution (Fermi temperature 2000 K) was applied to determine the molecular orbital occupations. It can avoid the oscillation problems during the search for a self-consistent solution, often appearing when DFTB energy for dissociated or close to dissociation system was calculated, which allows to recover the continuity in energy and gradients in the case of level crossing. \cite{Kukk2015} In the dynamics collision simulation, at the time of 200 fs, the Argon atom was given a velocity (0.0589 Å·fs$^{-1}$) corresponding to the 7.2 eV center of mass collision energy used in the experiment. \cite{Braud2019}. A series of dynamics collision simulation models were generated according to the distance between collision position and the center of size of the cluster. 600 dynamics collision simulations were performed every 0.5 Å from the center of size of each obtained lowest-energy cluster (H$_2$O)$_{n=3-7, 12}$UH$^+$ at molecular dynamics (MD) bath temperature 25 K. In case missing any collision, we set the biggest distance between collision position and the center of size of the cluster to be (R + 1) Å rather than the cluster radius R. So totally 600(2R + 3) simulations were calculated. Owing to cluster was set to rotate regularly during the generation of the models, the Ar atom can collide at almost all the possible positions of the cluster. The total simulation time was divided into 600(2R + 3)  segments of 15 ps duration for each (H$_2$O)$_{n=3-7, 12}$UH$^+$. After the dynamics collision computation ends of every segment, the geometry of the system was analyzed to detect the possible fragments. A dissociation was defined to arise when the smallest distance between the atoms of two fragments is larger than a given critical distance 5.0 Å.

\blue{i-PI?}



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\section{Results and Discussion} \label{resul_disc}
\textbf{The Distributions of the Initial Collision Models} In order to simulate the collision process of the obtained lowest-energy configuration of (H$_2$O)$_{n=3-7, 12}$UH$^+$ clusters with Ar, a reasonable construction of the collision models are needed. In our dynamics collision simulations, totally 2R+3 series were performed for every (H$_2$O)$_{n=3-7, 12}$UH$^+$ cluster. And 600 models were conducted in every series. For visualization, the distribution maps of the initial positions of Ar atom with respect to each (H$_2$O)$_{n=3-7, 12}$UH$^+$ cluster configuration were made. Here we take the collision of Ar to (H$_2$O)$_4$UH$^+$ cluster as an example, Figure \ref{fig:sphere} displays the collision models of the relative positions of Ar to the initial (H$_2$O)$_4$UH$^+$ cluster configuration of the first series that the collision positions are at the center of size of the cluster. As shown in Figure \ref{fig:sphere}, the sphere in picture a is composed of 200 relative positions of Ar to the initial (H$_2$O)$_4$UH$^+$ cluster configuration in the first series. The sphere in picture b is composed of 400 relative positions of Ar to the initial (H$_2$O)$_4$UH$^+$ cluster configuration in the first series and the sphere in picture c is composed of 600 relative positions of Ar to the initial (H$_2$O)$_4$UH$^+$ cluster configuration in the first series. From pictures a, b, and c in Figure \ref{fig:sphere}, it indicates the more simulations are performed, the more colliding opportunities at all the possible positions of (H$_2$O)$_4$UH$^+$ cluster Ar will have. As shown in picture d of Figure \ref{fig:sphere}, the outer layer of the sphere is the 200 relative Ar positions in the first series and the inner layer is the 200 relative Ar positions to the initial (H$_2$O)$_4$UH$^+$ cluster configuration in the last series (the distance between collision positions and the center of size of the cluster is R$_{(H_2O)_4UH^+}$ Å. The collision models of Ar and (H$_2$O)$_{n=3, 5-7, 12}$UH$^+$ clusters are displayed in Figure SX in the SI. In experiment, the collision positions are randomly, which means that Ar can reach any position of the clusters. All the collision model pictures of Ar and (H$_2$O)$_{n=3-7, 12}$UH$^+$ clusters shows our constructions for the collision simulation models are reliable and close to the collision situation in the experiment. With these reasonable models, the explicit collision simulations were conducted. To confirm the statistical convergence is reached, we compare the proportions of neutral uracil molecules loss and the total fragmentation cross sections of (H$_2$O)$_{n=3, 5-7, 12}$UH$^+$ clusters with those in experiment. As shown in Table S1 in SI, the data of 200 simulations, 400 simulations, and 600 simulations in every series for all (H$_2$O)$_{n=3, 5-7, 12}$UH$^+$ clusters were almost the same, which indicates 600(2R + 3) simulations are enough.

  \begin{figure}
  \includegraphics[width=0.4\linewidth]{figure/sphere}
     \centering
    \caption{Representation of initial Ar positions of the first series to perform collision simulations with the lowest-energy isomer of (H$_2$O)$_4$UH$^+$; For the first series, a: 200 representation of initial Ar positions; b: 400 representation of initial Ar positions; c: 600 representation of initial Ar positions; d: 200 representation of initial Ar positions of the first series and last series, separately.}
    \label{fig:sphere} 
 \end{figure}

\textbf{Proportion of Neutral Uracil Molecule Loss}

Formula of calculating the proportion of neutral uracil loss:

In this part, the proportion of neutral uracil molecule loss of each lowest-energy (H$_2$O)$_{n=3-7, 12}$UH$^+$ cluster by colliding with Ar atom will be discussed. No neutral uracil loss for (H$_2$O)$_{n=1-4}$UH$^+$, the evaporation of uracil starts at n=5, and becomes significant at n=6 were observed in experiment.\cite{Braud2019} In our calculations, the proportions of neutral uracil molecule loss extracted from 600(2R + 3) dynamics collision simulations for (H$_2$O)$_{n=3-7, 12}$UH$^+$ clusters were plotted in Figure \ref{fig:neutralUloss} as a function of number of water molecules n. As displayed in Figure \ref{fig:neutralUloss}, the overall trend of the proportion of neutral uracil molecule loss in theory is consistent with the one in experiment except the case n=5. The evaporation of neutral uracil molecule means the excess proton stayed in the water clusters. When n = 3-4, and 6-7 the neutral uracil loss increases with n. It indicates with the increase of the number of water molecules in the cluster, the excess proton is more likely to lie in the water cluster after collision. 

\begin{figure}
  \includegraphics[width=0.5\linewidth]{figure/Neutral_U_loss.eps}
  \centering
    \caption{Proportion of neutral uracil loss after collision of clusters (H$_2$O)$_{n=3-7, 12}$UH$^+$ with Ar from both theoretical (pink line) and experiment (green line) results.}
    \label{fig:neutralUloss} 
 \end{figure}

The neutral uracil molecule loss proportion, 0.0\%, of n = 3 in Figure \ref{fig:neutralUloss} is from the second lowest-energy isomer of (H$_2$O)$_3$UH$^+$ cluster shown in \ref{fig:3ato5d} (3b) that localization of the excess proton is on the uracil (U-H form). For the first lowest-energy isomer of (H$_2$O)$_3$UH$^+$ cluster (U-H form) shown in Figure \ref{fig:3ato5d} (3a), the proportion is 4.4\% (see Table \ref{tab:table1}), which is also very close to the one in experiment. The relative energy of 3a and 3b calculated at MP2/Def2TZVP level is only 0.3 kcal$\cdot$mol$^{-1}$. In experiment, the neutral uracil loss proportion of (H$_2$O)$_3$UH$^+$ cluster is about 1.0\%, which implies both the first and second lowest-energy isomers of (H$_2$O)$_3$UH$^+$ cluster are dominant. From the process of our dynamics collision simulations for (H$_2$O)$_3$UH$^+$ cluster with Ar, the dissociation occurred directly and the excess proton still stays on uracil. 
   
\begin{table}
  \begin{center}
    \caption{Neutral uracil loos proportion and total fragmentation cross section of different isomers of clusters (H$_2$O)$_{n=3-7, 12}$UH$^+$ (PNUL refers to the proportion of neutral uracil loss; TFCS refers to the total fragmentation cross section; LEP refers to the location of the excess proton; U-H refers to the excess proton is on the uracil; W-H-U refers to the excess proton is on the water cluster but adjacent to one oxygen atom of uracil; W-H refers to the excess proton is completely on the water cluster and far from uracil).}
    
    \label{tab:table1}
    \begin{tabular}{c|c|c|l} 
      \textbf{Cluster} & \textbf{PNUL (\%)} & \textbf{TFCS (Å$^2$)} & \textbf{LEP}\\
      \hline
      3a & 4.4 & 34.0 & U-H\\
      3b & 0.0 & 39.2 & U-H\\
      4a & 22.3 & 35.6 & W-H-U\\
      4b & 2.2 & 44.1 & U-H\\
      5a & 34.9 & 45.1 & W-H\\
      5b & 25.4 & 36.1 & W-H-U\\
      5c & 23.5 & 42.8 & W-H-U\\
      5d & 0.1 & 45.5 & U-H\\
      6a & 36.6 & 41.2 & W-H\\
      6b & 30.0 & 42.9 & W-H\\
      6c & 31.2 & 43.7 & W-H\\
      6d & 28.5 & 41.5 & W-H\\
      6e & 30.1 & 47.8 & W-H-U\\
      6f & 14.2 & 52.3 & W-H-U\\
      7a & 27.7 & 51.0 & W-H\\
      7b & 17.4 & 49.5 & W-H-U\\
      12a & 17.8 & 49.0 & W-H\\
      12x & 14.0 & 52.0 & W-H-U\\          
    \end{tabular}
  \end{center}
\end{table} 

\begin{figure}
  \includegraphics[width=0.8\linewidth]{figure/3ato5d}
  \centering
    \caption{Some lowest-energy configurations of clusters (H$_2$O)$_{n=3-5}$UH$^+$ (the distances are given in Å and relative binding energies are in kcal$\cdot$mol$^{-1}$.}
    \label{fig:3ato5d} 
 \end{figure}

The neutral uracil molecule loss proportion, 2.2\%, of n = 4 in Figure \ref{fig:neutralUloss} is from the second lowest-energy isomer of (H$_2$O)$_4$UH$^+$ cluster (U-H form) shown in Figure \ref{fig:3ato5d} (4b). The proportion is 22.3\% (see Table \ref{tab:table1}) for the first lowest-energy isomer (see 4a in Figure \ref{fig:3ato5d}) of (H$_2$O)$_4$UH$^+$ cluster (U-H form) that the excess proton is close to the water cluster but is still bounded to uracil, which is too high compared with the corresponding proportion 1.8\% in experiment. The relative energy of 4a and 4b calculated at MP2/Def2TZVP level is only 0.9 kcal$\cdot$mol$^{-1}$. For ((H$_2$O)$_4$UH$^+$ cluster, our dynamics collision simulations shows the collision leads a direct dissociation. This indicates the collision of the second lowest-energy isomer of (H$_2$O)$_4$UH$^+$ cluster is dominant and the excess proton in (H$_2$O)$_4$UH$^+$ cluster is sensitive but is still bounded to uracil. 

As displayed in Figure \ref{fig:neutralUloss}, the neutral uracil molecule loss proportion is 0.1\% for (H$_2$O)$_5$UH$^+$ cluster, which is from the fourth lowest-energy isomer (U-H form) shown in Figure \ref{fig:3ato5d} (5d). For the first lowest-energy configuration of (H$_2$O)$_5$UH$^+$ cluster that the localization of the excess proton is far from uracil and lies on the water cluster (W-H form) shown in Figure \ref{fig:3ato5d} (5a), the proportion is 34.9\% (see Table \ref{tab:table1}). For the second and third lowest-energy configurations of (H$_2$O)$_5$UH$^+$ cluster (U-H form) that the excess proton is close to water cluster but is still bounded to uracil shown in Figure \ref{fig:3ato5d} (5b, 5c), the proportion are 25.4\% and 23.5\% (see Table \ref{tab:table1}), separately. For clusters 5a, 5b, 5c, and 5d, our dynamics collision simulations show they have a direct dissociation after collision, thes explains why 5a has a higher proportion than other isomers. The relative energy of 5a and 5d calculated at MP2/Def2TZVP level is 2.4 kcal$\cdot$mol$^{-1}$, which is within the limit of error. From the neutral uracil molecule loss proportion of configurations 5a, 5b, 5c, and 5d the proportion of 5d, 0.1\%, is the closest to the one, 3.8\%, in experiment, it indicates the configuration that the excess proton lies on the uracil is dominant.

For (H$_2$O)$_6$UH$^+$ cluster, the neutral uracil molecule loss proportion is 14.2\% in Figure \ref{fig:neutralUloss}, which is from the sixth lowest-energy isomer (see 6f in Figure \ref{fig:6ato7b}) that the excess proton is bounded to water cluster but close to one oxygen atom of uracil (W-H-U form). For the first, second, third, fourth, and fifth lowest-energy configurations of (H$_2$O)$_6$UH$^+$ cluster (W-H form) (see 6a, 6b, 6c, 6d, and 6e in Figure \ref{fig:6ato7b}) and was separated by one water molecule from uracil, the proportion is 36.6\%, 30.0\%, 31.2\%, 28.5\%, and 30.1\% (see Table \ref{tab:table1}), respectively. The distances between OX and HX in 6a, 6c, 6d are 1.774 Å, 1.745 Å, 1.804 Å, and the distances between OY and HY in 6b and 6e are 1.660 Å and 1.614 Å, respectively. It implies that the neutral uracil loss proportion increases with the distance between uracil and the excess proton in (H$_2$O)$_6$UH$^+$ cluster, which is in line with the observation from dynamics collision simulations that (H$_2$O)$_6$UH$^+$ cluster has a direct dissociation after collision. The relative energy of 6a and 6f calculated at MP2/Def2TZVP level is 2.7 kcal$\cdot$mol$^{-1}$. From the neutral uracil molecule loss proportion of configurations 6a, 6b, 6c, 6d, 6e, and 6f, the proportion of 6f, 14.2\% is the closest to the one, 14.3\%, in experiment, it indicates the configuration that the excess proton is close to water clusters but is still bounded to uracil is dominant.

\begin{figure}
  \includegraphics[width=0.8\linewidth]{figure/6ato7b}
    \caption{Some lowest-energy configurations of clusters (H$_2$O)$_{n=6-7}$UH$^+$  (the distances are given in Å and relative binding energies are in kcal$\cdot$mol$^{-1}$.}
    \label{fig:6ato7b} 
 \end{figure}  
 
 \begin{figure}
  \includegraphics[width=0.5\linewidth]{figure/12ad.png}
  \centering
    \caption{Some lowest-energy configurations of clusters (H$_2$O)$_{12}$UH$^+$ (the distances are given in Å and relative binding energies are in kcal$\cdot$mol$^{-1}$ ).}
    \label{fig:12ad} 
 \end{figure}
 
Figure \ref{fig:neutralUloss} displays the neutral uracil molecule loss proportion 17.4\% of n=7, which is from the second lowest-energy isomer of (H$_2$O)$_7$UH$^+$ cluster (see 7b in Figure \ref{fig:6ato7b}) (W-H-U form).  As displayed in Figure \ref{fig:6ato7b}, the proportion of the first lowest-energy isomer 7a (W-H form) of (H$_2$O)$_7$UH$^+$ cluster is 27.7\% shown in Table \ref{tab:table1}. The proportion of 7b, 17.4\% is close to the experiment result 15.8\%. From the dynamics collision simulations process for (H$_2$O)$_7$UH$^+$ cluster, the direct dissociation is dominant. It implies the neutral uracil loss proportion is determined by the initial configuration of the cluster. The relative energy of 7a and 7b calculated at MP2/Def2TZVP level is only 0.3 kcal$\cdot$mol$^{-1}$. This indicates the exist of isomer 7b that the excess proton is between the water cluster and uracil plays a dominant role after collision.

From the determination conducted by Zamith’s \textit{et al.}, the neutral uracil loss proportion starts to decrease from n=9,\cite{Braud2019} this attracted us to perform the dynamics collision simulation of big cluster (H$_2$O)$_{12}$UH$^+$ as an example to explore why it has this change. For cluster  (H$_2$O)$_{12}$UH$^+$, Figure \ref{fig:neutralUloss} displays the neutral uracil molecule loss proportion, 14.0\%, which is from the sixth lowest-energy isomer. For the first lowest-energy isomer 12a (W-H form, see 12a in Figure \ref{fig:12ad}), the corresponding proportion is 6.1\%. The neutral uracil loss proportions of the second and fifth are 17.8\% and 3.7\%, separately. From 12a in Figure \ref{fig:12ad}, we can see the uracil in 12a is belong to the di-keto form (there is a hydrogen atom on each nitrogen of uracil), and the excess proton was separately by one water molecule from uracil, additionally, the uracil is surrounded by the water cluster, all of these lead the excess proton to go to the near oxygen atom of uracil. So the neutral uracil loss proportion of 12a is only 6.1\%. For 12b the excess proton is on the water cluster and very far from the uracil (W-H form, see 12b in Figure \ref{fig:12ad}), which leads to a ralative high neutral uracil loss proportion (17.8\%). For 12e in Figure \ref{fig:12ad} (W-H-U form), the distance between the excess proton \blue{HX and OY} is 1.575 Å, and the uracil is surrounded by the water cluster so the neutral uracil loss proportion is very low (3.7\%). For 12f (W-H-U form, the distance between the excess proton \blue{HX and OY} is 1.624 Å, and the uracil is not surrounded by the water cluster (see 12f in Figure \ref{fig:12ad}), which leads a higher neutral uracil loss proportion (14.0\%) than that of 12e. From the results of 12a, 12b, 12e, and 12f, it indicates for cluster (H$_2$O)$_{12}$UH$^+$, the initial configurations also play an important role for the dissociation products. 

Through comparing the neutral uracil molecule loss proportion of different W-H form clusters: the proportion of 5a (34.9\%), 6a (36.6\%), 7a (27.7\%), and 12b (17.8\%), it’s clear that with the increase of the number of water molecules in mixed clusters the evaporation of neutral uracil decrease; especially for big cluster (H$_2$O)$_{12}$UH$^+$, the neutral uracil loss has a significant reduction, this implies it has a structure rearrangement prior to dissociation. For 6f and 12f (W-H-U form), the loss of neutral uracil of 12f is lower than it of 6f,  which also indicates the structure rearrangements occur in 12f. The proportion of 12f, 14.0\%,  is closer to the one, 12.2\%, in experiment than 17.8\% of 12a and the relative energy of 12a and 12f calculated at MP2/Def2TZVP level is only 2.4 kcal$\cdot$mol$^{-1}$, which shows that the collision of 12f with Ar plays a dominant role. So for (H$_2$O)$_{12}$UH$^+$ cluster, both the direct dissociation and with structural rearrangements prior to dissociation are dominant after collision. 

From Table \ref{tab:table1}, we can see for clusters (H$_2$O)$_{n=3-4}$UH$^+$ with U-H form, the proportions of neutral uracil loss are about 0.0\%. For different isomers of clusters (H$_2$O)$_{n=5-7}$UH$^+$ with the W-H form, they have a relative high proportion. For clusters (H$_2$O)$_{n=4-7}$UH$^+$ with W-H-U form, they have a relative low proportion and the proportion decreases with distance between the excess proton and the adjacent oxygen atom of uracil. For cluster (H$_2$O)$_{12}$UH$^+$, when the excess proton has the W-H form localization, it also has a higher proportion of neutral uracil loss than the one when the excess proton is the W-H-U form. In general, for any cluster of (H$_2$O)$_{n=3-7, 12}$UH$^+$, the neutral uracil loss proportion has a direct relationship with the localization form of the excess proton: proportion (W-H form) $>$ proportion (W-H-U form) $>$ proportion (U-H form). In other words, it is obvious that the neutral uracil loss proportions of clusters (H$_2$O)$_{n=3-7, 12}$UH$^+$ are significantly affected by the initial configuration of the clusters. However, for cluster (H$_2$O)$_{12}$UH$^+$, even the excess proton is the W-H form, it didn’t have a too high proportion owing to the structural rearrangements that the excess proton goes back to uracil after collision of cluster (H$_2$O)$_{12}$UH$^+$ and Ar. It’s worth noticing that why cluster (H$_2$O)$_{12}$UH$^+$ has structural rearrangements prior to dissociation. We propose for cluster (H$_2$O)$_{12}$UH$^+$, there are more hydrogen bonds than the small clusters, which needs more energy to lose water molecules, so the proton has time to go back to uracil before dissociation.

\textbf{Total Fragmentation Cross Section} Formula of calculating the cross section:

In the light of the results of 600(2R + 3) dynamics collision simulations for each lowest-energy (H$_2$O)$_{n=3-7}$UH$^+$ cluster, the total fragmentation cross sections of the (H$_2$O)$_{n=3-7}$UH$^+$ clusters were determined and compared with those in experiment. As shown in Table \ref{tab:table1}, for different isomers of lowest-energy (H$_2$O)$_{n=3-7, 12}$UH$^+$ clusters, the total fragmentation cross sections are very close. So in this part, we only discuss the total fragmentation cross section of the lowest-energy (H$_2$O)$_{n=3-7}$UH$^+$ cluster who has the closest neutral uracil loss proportion compared with the one in experiment.

The total fragmentation cross sections of mixed (H$_2$O)$_{n=3-7}$UH$^+$ clusters from our simulation results of collision with Ar and the corresponding experiment results are plotted in Figure \ref{fig:crosssection} as a function of the number of water molecules n at 7.2 eV center of mass collision energy. As displayed in Figure \ref{fig:crosssection}, the curves in theory and in experiment have the same overall trend that the total fragmentation cross sections of mixed (H$_2$O)$_{n=3-7}$UH$^+$ clusters increase according to the number of water molecules. This indicates when the size of the clusters increase, the Ar and the cluster has a higher opportunity to collide. For (H$_2$O)$_7$UH$^+$ cluster, the value in theory is slightly lower than the one of (H$_2$O)$_6$UH$^+$ cluster but the difference is only 1.3 Å$^2$, which is within the limit of error. Additionally, the absolute value of total fragmentation cross sections of (H$_2$O)$_{n=3-7}$UH$^+$ clusters in theory and experiment are close to each other. The biggest and smallest differences of the total fragmentation cross section for (H$_2$O)$_{n=3-7}$UH$^+$ clusters are 7.0 and 1.5 Å$^2$, separately between our calculation results and those in the experiment. Those results imply our simulations results are good enough.

If it needs to make a further detailed description of the total fragmentation cross sections? 
 
 \begin{figure}
  \includegraphics[width=0.5\linewidth]{figure/cross-section.eps}
  \centering
    \caption{Total fragmentation cross section in both theory (pink line) and experiment (green line) of clusters (H$_2$O)$_{n=3-7}$UH$^+$ who the closest neutral uracil loss proportion compared with those in experiment.}
    \label{fig:crosssection} 
 \end{figure}
 
\textbf{Mass Spectrum of Fragments with Excess Proton}
Formula of calculating the fragment ratio:

To explore the collision products, the branching ratios (intensity) of different fragments with the excess proton were extracted from the dynamics collision simulations and compared with the mass spectrum obtained by colliding cluster (H$_2$O)$_7$UH$^+$ with Ne at 7.2 eV center of mass collision energy in experiment.\cite{Braud2019} Figure\ref{fig:mass_spec} displays the specific fragment ratio in the total fragments from the collision of the second lowest-energy cluster (H$_2$O)$_7$UH$^+$ with Ar. Fragments (H$_2$O)$_{n=3-5}$H$^+$ were not found in our calculation, which agrees with the very low intensity of fragments (H$_2$O)$_{n=3-5}$H$^+$ in experiment. This implies when (H$_2$O)$_{n=3-5}$ leave, they don’t have enough proton affinity to take away the excess proton. The intensity of fragments (H$_2$O)$_{n=6-7}$H$^+$ are higher than fragments (H$_2$O)$_{n=3-5}$H$^+$ in experiment results and we also  determined the fragments (H$_2$O)$_{n=6-7}$H$^+$ in our calculation, which indicate the proton affinity of (H$_2$O)$_{n=6-7}$ is higher than (H$_2$O)$_{n=3-5}$ that in line with the previous study. \cite{Magnera1991}

As shown in Figure \ref{fig:mass_spec}, we didn’t get UH$^+$ but it was detected in experiment with time of flight 60 $\mu$s. For each dynamics collision simulation of cluster (H$_2$O)$_7$H$^+$ was performed with simulation time 15 ps, we cannot assert that the UH$^+$ will not appear in longer simulation. Modeling the complete duration of the experiment (up to $\mu$s) is out of reach with MD/SCC-DFTB simulations. Additionally, we calculated the energy of (H$_2$O)$_6$H$^+$, which is from (H$_2$O)$_7$H$^+$ cluster with the dissociation of one water after collision with Ar at SCC-DFTB level (see Table \ref{tab:fragenergy}). We also calculated the lowest energies of (H$_2$O)$_5$H$^+$ and water (see Table \ref{tab:fragenergy}). From the data in Table \ref{tab:fragenergy}, the relative energy $\Delta$E between energy of (H$_2$O)$_6$H$^+$ and lowest energy of (H$_2$O)$_5$H$^+$ plus H$_2$O can reach 1.007 eV, so it is possible for the fragment (H$_2$O)$_6$H$^+$ to lose more water molecules. From this, we suggest if the dynamics collision simulation is long enough, finally UH$^+$ can be obtained. 

As displayed in Figure \ref{fig:mass_spec}, the intensity of fragments (H$_2$O)$_{n=2-4}$UH$^+$ increase with the number of n which is in line with the results in experiment. It indicates the second lowest-energy cluster (H$_2$O)$_7$UH$^+$ has more chances to lose three water molecules than to lose six water molecules. The intensity of fragment (H$_2$O)$_5$UH$^+$ is close to it of fragment (H$_2$O)$_4$UH$^+$ in theory which agree with the one in experiment. The intensity of fragment (H$_2$O)$_6$UH$^+$ increases a lot compared with these of (H$_2$O)$_{n=2-5}$UH$^+$ in the calculated results but it is not so high in experiment, which indicates in our simulations, the  dissociation of the second lowest-energy cluster (H$_2$O)$_7$UH$^+$ losing one water molecule is dominant. The parent cluster (H$_2$O)$_7$UH$^+$ has the highest ratio among all fragments, which is fully consistent with it in experiment. From the analyses of the mass spectrum in theory and experiment, it implies our simulations can quantitatively describe the fragment ratios.

\begin{figure}  
 \centering
 \begin{subfigure}
 \centering
 \includegraphics[width=0.4\linewidth]{figure/mass_spec.eps}
% \raggedright
   \label{fig:sub1}
   \end{subfigure}
   \begin{subfigure}
   \centering
   \includegraphics[width=0.45\linewidth]{figure/mass-experiment.png}
   \label{fig:sub2}
   \end{subfigure}

    \caption{(a): Mass spectrum in theory of the charged fragments from the second lowest-energy cluster (H$_2$O)$_7$UH$^+$ with simulation time 15 ps (fragments (H$_2$O)$_n$H$^+$ are in red and fragments U(H$_2$O)$_n$H$^+$ are in blue); (b): Mass spectrum of the charged fragments of cluster (H$_2$O)$_7$UH$^+$ in experiment.}
    \label{fig:mass_spec} 
 \end{figure}


%\begin{table}
%  \begin{center}
%    \caption{Fragment ratios in the total fragments from the %dissociation of the second lowest-energy cluster (H$_2$O)$_7$UH$^+$ % with simulation time 15 ps.}      
%     \label{tab:massspectrum}
%     \begin{tabular}{c|c} 
%      \textbf{Fragment} & \textbf{Ratio (\%)} \\
%       \hline
% %       (H$_2$O)$_3$H$^+$ & 0.00 \\
%       (H$_2$O)$_4$H$^+$ & 0.00 \\
%       (H$_2$O)$_5$H$^+$ & 0.00 \\
%       (H$_2$O)$_6$H$^+$ & 2.62 \\
% %       (H$_2$O)$_7$H$^+$ & 2.14 \\
%        UH$^+$       & 0.00 \\
%       (H$_2$O)UH$^+$ & 0.07 \\
%       (H$_2$O)$_2$UH$^+$ & 0.41 \\
%       (H$_2$O)$_3$UH$^+$ & 1.60 \\
% %      (H$_2$O)$_4$UH$^+$ & 3.66 \\
%       (H$_2$O)$_5$UH$^+$ & 7.56 \\
%       (H$_2$O)$_6$UH$^+$ & 18.09 \\
%       (H$_2$O)$_7$UH$^+$ & 63.83 \\     
%    \end{tabular}
%   \end{center}
% \end{table} 

\begin{table}
  \begin{center}
    \caption{Energies of different (H$_2$O)$_6$UH$^+$ fragments selected from the dissociation of the second lowest-energy cluster (H$_2$O)$_7$UH$^+$ at SCC-DFTB level, and the lowest energies (H$_2$O)$_5$UH$^+$ and (H$_2$O) at SCC-DFTB level. The relative energy $\Delta$E = E$_{(H_2O)_6UH^+}$ -(E$_{(H_2O)_5UH^+}$ + E$_{H_2O}$) . All energies here are given in eV.}      
    \label{tab:fragenergy}
    \begin{tabular}{c|c|c|c} 
      \textbf{E$_{(H_2O)_6UH^+}$} & \textbf{E$_{(H_2O)_5UH^+}$} & \textbf{E$_{H_2O}$} & \textbf{$\Delta$E}\\ 
      \hline
      -44.361 &  -40.312 & -4.06 & 0.190 \\
      -44.331 &  -40.312 & -4.06 & 1.007 \\
      -44.334 &  -40.312 & -4.06 & 0.925 \\
    \end{tabular}
  \end{center}
\end{table} 

 \begin{figure}
  \includegraphics[width=0.8\linewidth]{figure/proporEachFrag-7-2.eps}
  \centering
    \caption{The proportions of the main fragment from the dissociation of the second lowest-energy parent cluster (H$_2$O)$_7$UH$^+$.}
    \label{fig:proporEachFrag-7-2} 
 \end{figure}

 \begin{figure}
  \includegraphics[width=0.8\linewidth]{figure/proporEachFrag-12-6.eps}
  \centering
    \caption{The proportions of the main fragment from the dissociation of the sixth lowest-energy parent cluster (H$_2$O)$_{12}$UH$^+$.}
    \label{fig:proporEachFrag-12-6} 
 \end{figure}

 \begin{figure}
  \includegraphics[width=0.8\linewidth]{figure/proporEachFrag-12-5-s1.eps}
  \centering
    \caption{The proportions of the main fragment from the dissociation of the fifth lowest-energy parent cluster (H$_2$O)$_{12}$UH$^+$.}
    \label{fig:proporEachFrag-12-5-s1} 
 \end{figure}

\begin{figure}
  \includegraphics[width=0.8\linewidth]{figure/proporEachFrag-12-2-s1.eps}
  \centering
    \caption{The proportions of the main fragment from the dissociation of the second lowest-energy parent cluster (H$_2$O)$_{12}$UH$^+$.}
    \label{fig:proporEachFrag-12-2-s1} 
 \end{figure}

  
\textbf{Time-Dependent Proportion of Each Fragment}

In addition, the time-dependent proportion of each fragment was extracted from 600(2R + 3) dynamics collision simulations. Here we take the time-dependent proportion of each fragment from the dissociation second lowest-energy parent cluster (H$_2$O)$_7$UH$^+$ and the sixth lowest-energy parent cluster (H$_2$O)$_{12}$UH$^+$ as an example. For the sake of seeing clearly, only the main fragment proportions plotted as a function of simulation time are showed in Figure 7. The proportions of the main fragment of clusters (H$_2$O)$_{n=3-6}$UH$^+$ are shown in SI Figure SX. From Figure \ref{fig:proporEachFrag_7_2}, it is clear that the parent cluster (H$_2$O)$_7$UH$^+$ exists from the beginning and different fragments starts to appear after collision. It can be seen when the collision is finished, the fragment proportions almost doesn’t change any more. It is worth noticing the fragment (H$_2$O)$_6$UH$^+$ increase first and then it decreases, which indicates there are water molecules dissociated from it. For fragment proportios of cluster (H$_2$O)$_{12}$UH$^+$, from Figure \ref{fig:proporEachFrag_12_6}, it shows fragments 
(H$_2$O)$_{11}$UH$^+$ and (H$_2$O)$_{10}$UH$^+$ increase at the beginning and then decrease, and finally they tend to be steady. The second and the third or more times dissociation after collision and all the main fragment proportion do not tend to a constant so fast imply that there are more chances to rearrange prior to complete dissociation.

From the time-dependent proportion of each fragment from clusters (H$_2$O)$_{n=3-6, 12}$UH$^+$, it confirms that up to 7 water molecules a direct dissociation mechanism occurs. For cluster (H$_2$O)$_{12}$UH$^+$, it undergoes structural rearrangements prior to dissociation, which is proof of a statistical dissociation mechanism.



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\section{Conclusions} \label{Concl}



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\begin{acknowledgement}
The authors acknowledge the supercomputing facility of CALMIP for generous allocation
of computer resources (projects P1320 and P0059). The authors declare that there has
been no significant financial support for this work.
\end{acknowledgement}

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